The function is $\"\"$ .

Graph :

Graph the function $\"\"$ :

$\"\"$

Observe the graph.

The horizontal asymptote is at $\"\"$ .

The function is $\"\"$ .

To find the horizontal asymptote, evaluate the limit of the function as $\"\"$ .

$\"\"$

Therefore the horizontal asymptote is at $\"\"$ .

Discrepancy :

In practical, limit of the function is $\"\"$ , but from the graphing device the horizontal asymptote occurs at $\"\"$ .

So the reason of this discrepancy is the interval of the graph is too small, to show the behavior of the function for a large values of $\"\"$ .

The horizontal asymptote is at $\"\"$ .